Details

sample118.0ms

Algorithm

intervals

Results

57.0ms	125×	body	1280	valid
18.0ms	256×	pre	80	true
16.0ms	65×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	43×	body	80	valid
1.0ms	8×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(- (tan (+ y z)) (tan a))
0.2b	(+ x (- (tan (+ y z)) (tan a)))
3.8b	(tan (+ y z))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
5×	`add-sqr-sqrt`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sub-neg` `tan-sum` `associate-+r+` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 42

Calls

3 calls:

7.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(+ x (- (tan (+ y z)) (tan a)))
4.0ms	(tan (+ y z))

series281.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(- (tan (+ y z)) (tan a))
118.0ms	(+ x (- (tan (+ y z)) (tan a)))
52.0ms	(tan (+ y z))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	196	346
1	467	335
2	1316	334
3	5002	334

prune147.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Merged error: 0.1b

Counts

52 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
2×	`+-commutative` `sub-neg` `associate-+r+` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `flip3--` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 67

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
12.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
14.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
6.0ms	(* (tan y) (tan z))

series882.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (tan y) (tan z))
369.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
332.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
91.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	367	860
1	1074	821
2	3057	814
3	5001	814

prune273.0ms

Filtered

79 candidates to 59 candidates (74.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	70	9	79
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin y) (cos z))
0.2b	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))
0.2b	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
9×	`add-log-exp`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`tan-quot`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `associate-+r+` `flip3-+` `div-exp` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `frac-times` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `associate-l/` `clear-num` `associate-/r*` `associate-/r/` `cos-mult` `sin-cos-mult` `div-inv` `distribute-lft-out--`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (sin y) (cos z))
19.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
6.0ms	(* (tan y) (tan z))
10.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin y) (cos z))
328.0ms	(+ x (- (/ (/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
87.0ms	(* (tan y) (tan z))
143.0ms	(/ (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (* (cos y) (cos z)))

simplify51.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	479	1163
1	1735	1026
2	5001	1026

prune391.0ms

Filtered

93 candidates to 67 candidates (72.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 0.1b

Counts

103 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (tan y) (tan z)) (cos a))
0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

19×	`associate-*l/`
18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`tan-quot` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`associate-/l/`
6×	`frac-sub`
5×	`flip3--` `flip--`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3-+` `times-frac` `pow-prod-down` `frac-add` `-commutative` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `div-sub` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

8.0ms	(* (+ (tan y) (tan z)) (cos a))
5.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
15.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (+ (tan y) (tan z)) (cos a))
90.0ms	(* (tan y) (tan z))
89.0ms	(* (tan y) (tan z))
458.0ms	(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))

simplify74.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	587	1304
1	2701	1144
2	5003	1128

prune387.0ms

Filtered

108 candidates to 83 candidates (76.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	108	10	118

Merged error: 0.1b

Counts

118 → 10

regimes356.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	20
1	26	20

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3900×	body	1280	valid
536.0ms	8000×	pre	80	true
509.0ms	2016×	body	640	valid
115.0ms	665×	body	320	valid
59.0ms	1150×	body	80	valid
32.0ms	269×	body	160	valid